1. Field of the Invention
The invention relates to a method and circuit configuration for avoiding overflows in an adaptive, recursive digital wave filter including a transfer filter and a gradient filter, wherein the transfer filter and the gradient filter each have an adaptor with a given coefficient.
Adaptive filters are of major significance in many areas of discrete-time signal processing, particular in the fields of systems analysis, echo compensation in two-wire/four-wire transitions, line distortion correction and speech processing. In comparison with constant filters, it is a characteristic of such adaptive filters that the filter parameters which determine the transfer properties are optimally adjusted with respect to a Q function. Such a Q function is obtained, for instance, by minimizing the mean quadratic error of the output signal at the adaptive filter with respect to a reference signal. In typical methods, the partial derivations (gradient of the Q function are formed in accordance with the filter parameters to be adapted. For most quality criteria, that method is traceable to the formation of the partial derivations of the output signal of the adaptive filter in accordance with the filter parameters.
2. Description of the Related Art
Co-pending U.S. application Ser. No. 525,163, filed May 17, 1990, discloses a method and a configuration for performing the method, with which the gradient of the output signal of a discrete-time network, such as a filter, can be obtained with respect to the network or filter parameters. The gradient signal sought appears at the output of a gradient network that is supplied with internal signals of the network. The method or configuration becomes particularly simple for linear networks, because the gradient network has essentially the same structure as the given network. As a result, an expensive network synthesis becomes unnecessary. Further simplification is obtained for digital filters that are constructed solely with two-gate adaptors as well as for digital filters in which the network parameters are multiplication coefficients.
Digital wave filters known from German Patent DE-PS 20 27 303, corresponding to U.S. Pat. No. 3,967,099, for instance, are formed solely of time-lag elements and adaptors, which in turn are composed of adders or subtractors and multipliers. Various transfer functions can be adjusted with the aid of the multiplication coefficients. If the digital wave filters are used as adaptive filters, the coefficients are variable. The coefficients can be adjusted automatically to the desired optimal value by various methods, for instance the gradient method. In order to do this, the derivations of the filter output signal in accordance with the various coefficients are required. Such values can be determined with gradient filters in accordance with co-pending U.S. application Ser. No. 525,163, filed May 17, 1990. The gradient filters are likewise constructed as digital wave filters. Thus the gradient filters are formed of adaptors and time-lag elements. The input signal of the gradient filter is the product of the input signal of the multiplier for multiplication with one of the coefficients that determine the transfer behavior at a time. The output signal of the gradient filter is then the corresponding gradient of the output signal of the transfer filter with respect to the filter parameter or with respect to the coefficient.
When constructing the digital wave filters, the processing width of adders, subtractors and multipliers set limits on the representation range of the digital signals. In digital wave filters having fixed point arithmetic, the representable signal range is limited to the range of -1.ltoreq.x.ltoreq.1-2.sup.-n, where n is the processing width and x is the representable signal. An overflow occurs in the event that the results of the additions exceed the available range, making the outcome incorrect.
For an adaptor of a digital wave filter, the following equation applies: EQU b.sub.2 =(1-.mu.).multidot.a.sub.1 +.mu..multidot.a.sub.2 ( 1)
where a.sub.1 and a.sub.2 are the input signals and .mu. is given multiplier coefficient, which can assume values between 0 and 1. Since the amounts of the input signals are .vertline.a.sub.1 .vertline. 1 and .vertline.a.sub.2 .vertline. 1, the following inequalities apply for the amount of the output signal .vertline.b.sub.2 .vertline.: EQU .vertline.b.sub.2 .vertline..ltoreq.(1-.mu.).multidot..vertline.a.sub.1 .vertline.+.mu..multidot..vertline.a.sub.2 .vertline. (2a) EQU .vertline.b.sub.2 .vertline..ltoreq.(1-.mu.)+.mu. (2b) EQU .vertline.b.sub.2 .vertline..ltoreq.1. (2c)
This assures that under no circumstances can the adaptor cause overflows for the output signal b.sub.2. However, this is not true for the corresponding adaptor of the gradient filter, because: EQU b.sub.2 '=a.sub.1 '+.mu..multidot.a.sub.2 ' (3a) EQU .vertline.b.sub.2 '.vertline..ltoreq..vertline.a.sub.1 '.vertline.+.mu..multidot..vertline.a.sub.2 '.vertline. (3b) EQU .vertline.b.sub.2 '.vertline..ltoreq.1+.mu.. (3c)
As is apparent from equations 3a-3c, the output signal b.sub.2 ' of the subadaptor of the gradient filter is certainly capable of overflowing. Even if the input signal a.sub.1 ' is scaled with a factor d between zero and one, nevertheless an overflow occurs for the output signal b.sub.2 ', if .mu. is in the range of 1-d&lt;.mu..ltoreq.1.
It is accordingly an object of the invention to provide a method and circuit configuration for avoiding overflows in an adaptive, recursive digital wave filter having fixed point arithmetic, which overcome the hereinafore-mentioned disadvantages of the heretofore-known methods and devices of this general type and which avoid overflows in the gradient filter of the adaptive, recursive digital wave filter.